Subgroups — D₅₇×D₁₀₃ #37553607

Order 23484.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₈₇₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₀₃×D₅₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₉×D₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₉×D₁₀₃	—	3	1	no	maximal, Hall
5	C₃×C₁₉×C₁₀₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₉₅₇	—	3	1	no	—
7	C₁₉×D₁₀₃	D₃	1	1	yes	characteristic, complemented
8	D₁₉×C₁₀₃	—	3	1	no	—
9	C₁₉×C₁₀₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	D₃×D₁₀₃	—	19	1	no	maximal, Hall
11	D₃₀₉	—	19	1	no	—
12	C₃×D₁₀₃	D₁₉	1	1	yes	characteristic, complemented
13	D₃×C₁₀₃	—	19	1	no	—
14	C₂×D₁₀₃	—	57	1	no	Hall
15	C₃×C₁₀₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
16	C₂×D₅₇	—	103	1	no	maximal, Hall
17	C₂×C₁₀₃	—	57	1	no	—
18	D₁₀₃	—	57	1	no	—
19	D₁₀₃	D₅₇	1	1	yes	characteristic, direct product factor
20	C₂×C₃×C₁₉	—	103	1	no	—
21	D₅₇	—	103	1	no	—
22	D₅₇	D₁₀₃	1	1	yes	characteristic, direct product factor
23	C₁₀₃	C₂×D₅₇	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₁₉	—	309	1	no	Hall
25	C₃×C₁₉	C₂×D₁₀₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₉	—	103	1	no	—
27	D₁₉	—	3	1	no	—
28	D₁₉	—	309	1	no	—
29	C₁₉	D₃×D₁₀₃	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₃	—	1957	1	no	Hall
31	C₂×C₃	—	103	1	no	—
32	D₃	—	19	1	no	—
33	D₃	—	1957	1	no	—
34	C₂²	—	5871	1	no	Sylow
35	C₃	D₁₉×D₁₀₃	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	57	1	no	—
37	C₂	—	103	1	no	—
38	C₂	—	5871	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₉×C₁₀₃	C₂²
LCS	G ▷ C₃×C₁₉×C₁₀₃
UCS	C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. D₅₈₇₁	C₂	semidirect
2. C₁₀₃×D₅₇	C₂	semidirect
3. C₃×C₁₉×D₁₀₃	C₂	semidirect
5. C₃×C₁₉×C₁₀₃	C₂²	semidirect
7. C₁₉×D₁₀₃	D₃	semidirect
9. C₁₉×C₁₀₃	C₂×D₃	semidirect
12. C₃×D₁₀₃	D₁₉	semidirect
15. C₃×C₁₀₃	C₂×D₁₉	semidirect
19. D₁₀₃	D₅₇	direct (N × H)
22. D₅₇	D₁₀₃	direct (N × H)
23. C₁₀₃	C₂×D₅₇	semidirect
25. C₃×C₁₉	C₂×D₁₀₃	semidirect
29. C₁₉	D₃×D₁₀₃	semidirect
35. C₃	D₁₉×D₁₀₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₅₈₇₁	2
C₁₀₃×D₅₇	2
C₃×C₁₉×D₁₀₃	2
D₁₉×D₁₀₃	3
D₃×D₁₀₃	19
C₂×D₅₇	103

Subgroups — D57×D103 #37553607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₇×D₁₀₃ #37553607